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EXAMPLE
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F(n) mod 1 {0},
F(n) mod 2 {0,1,1},
F(n) mod 3 {0,1,1,2,0,2,2,1},
F(n) mod 4 {0,1,1,2,3,1},
F(n) mod 5 {0,1,1,2,3,0,3,3,1,4,0,4,4,3,2,0,2,2,4,1},
F(n) mod 6 {0,1,1,2,3,5,2,1,3,4,1,5,0,5,5,4,3,1,4,5,3,2,5,1},
F(n) mod 7 {0,1,1,2,3,5,1,6,0,6,6,5,4,2,6,1},
F(n) mod 8 {0,1,1,2,3,5,0,5,5,2,7,1},
F(n) mod 9 {0,1,1,2,3,5,8,4,3,7,1,8,0,8,8,7,6,4,1,5,6,2,8,1},
F(n) mod 10 {0,1,1,2,3,5,8,3,1,4,5,9,4,3,7,0,7,7,4,1,5,6,1,7,8,5,3,8, 1,9,0,9,9,8,7,5,2,7,9,6,5,1,6,7,3,0,3,3,6,9,5,4,9,3,2,5,7,2,9,1}.
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